EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...

If I have a Lorentz invariant equation of motion, like Klein-Gordon equation, is the solution automatically guaranteed to be Lorentz invariant?
I ask this question because of the discussion from Mark ...

I have a few questions to figure out Peskin 4.3 problem which is Linear sigma model about the interactions of pions at low energy. This model consist of N scalar fields governed by the Hamiltonian ($ ...

If we have that $$\delta \psi_L = i \epsilon_L^aT_a\psi_L$$
and $$\delta \psi_R = i \epsilon_R^aT_a\psi_R$$
And then we say that the above can be written in terms of $\epsilon^a$ and $\epsilon^a_5$ ...

In general, the gapless Goldstone mode is related to the "continuously" degenerate ground states. The Mexican hat potential is an example (see the logo of this SE website), where the bottom circle is ...

I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the ...

It is well known that the most of the proton (or any other hadron with light quarks) mass is not made up from quark masses, but it is dynamically generated by QCD mess inside. I've also heard that, ...

Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its ...

Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive ...

Followings are two independent questions as implied by the title:
(1) Considering a quantum Hamiltonian $H$ possesses some symmetries described by a symmetry group $G=\left \{ g_1,g_2,...,g_n \right ...

I'm trying to understand the symmetry content of the conductivity matrix: one information is, presence of time-reversal symmetry causes the off-diagonal terms to vanish. When this is broken (e.g. in ...

I have been assigned a presentation on a part of a paper (http://arxiv.org/abs/1303.6942). My task is to present on the spin and valley symmetries in graphene, and relate it back to the paper above.
...

What is the Hamiltonian 'H' (at the atomic or molecular level) that governs the phase transition from a liquid to a solid state? Actually, I want to explicitly verify the Hamiltonian 'H' admits the ...

I'm not familiar with QCD, but I'm looking for intuitive explanation of this phenomenon (it could be that easy explanation does not exist).
What I've read is that large part of hadron masses arises ...

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev.
In the case of the EW symmetry breaking, one can directly read the ...